Tensor Learning for Image Processing - Part 1

Many classical signal processing methods rely on representation and computation in the form of vectors and matrices, where multi-dimensional signal is unfolded into matrix for processing. The multi-linear structure would be lost in such vectorization or matricization, which leads to sub-optimal performance in processing.

In fact, a natural representation for multi-dimensional data is tensor. Avoiding multi-linear data structure loss, tensor computation can bring enhancement of a number of classical data processing techniques. As a typical kind of multi-dimensional data, image could be more efficiently and effectively processed by tensor learning techniques.

This tutorial will first provide a basic coverage of tensor notations, preliminary operations, main tensor decompositions and their properties. Based on them, a series of tensor learning methods are presented, as the multi-linear extensions of classical sparse component analysis, dictionary learning, missing component analysis, principle component analysis, linear regression, non-negative component analysis, subspace cluster, etc. The experimental results for a number of image processing applications are given, such as image reconstruction, image denoising, illumination normalization, background extraction, pose estimation, image fusion, image classification, etc. Finally, some tensor based deep neural networks are discussed for image processing applications.